The influence of time-dependent hydrodynamics on polymer centre-of-mass motion

We describe simulations of isolated ideal polymer chains consisting of N monomers. The solvent is simulated using a dissipative ideal gas maintained at a set temperature by a Lowe-Andersen thermostat. By choosing a particular ratio of the Kuhn length to the monomer hydrodynamic radius, long-polymer scaling of the diffusion coefficient holds even for chains composed of a few beads. However, this requires that the model capture the hydrodynamics correctly on length scales equivalent to a typical solvent particle separation. It does. The decay of the centre-of-mass velocity autocorrelation function, $C(t)$, for short chains scales rapidly to a function independent of N, so we can determine the long-polymer limit of the function. At long times it decays with an algebraic long-time tail of the form $C(t)\sim t^{-3/2}$. This is consistent with the predictions of theories that take into account the time dependence of the intra-polymer hydrodynamic interactions. We argue that the scaling of the decay implies that the intra-polymer hydrodynamic interactions propagate on a surprisingly rapid time scale.